Download Mathematics Intervention, Grades 6-12 4

LOS ANGELES UNIFIED SCHOOL DISTRICT
Division of Special Education
Extended School Year: Mathematics Intervention, Grades 6-12
493125 ESY Intervention Math (ESY MATH)
2.5 elective credits
Course Description
This elective course focuses on the individual student goals identified in the Individualized Education Program
(IEP) in the areas of number sense, algebra and functions, measurement and geometry, statistics, data analysis,
and probability, and mathematical reasoning. It is designed to minimize regression of prior learned skills. The
instructional focus is on intervention in reading, writing, speaking, listening, and language. The curriculum
consists of the use of evidence-based instruction and programs in these mathematics domains. LAUSD Division
of Special Education will provide teachers with curriculum, instructional pacing plans, and assessments that will
be used daily in the course.
Representative Standards- Common Core State Standards (Anchor Standards)
Standards for
Mathematical
Practice –
All Grades
Grade 6
Grade 7
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Ratios and Proportional Relationships: Understand ratio concepts and use ratio reasoning to solve
problems.
The Number System:
 Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
 Compute fluently with multi-digit numbers and find common factors and multiples.
 Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations:
 Apply and extend previous understandings of arithmetic to algebraic expressions.
 Reason about and solve one-variable equations and inequalities.
 Represent and analyze quantitative relationships between dependent and independent variables.
Geometry: Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability:
 Develop understanding of statistical variability.
 Summarize and describe distributions.
Ratios and Proportional Relationships: Analyze proportional relationships and use them to solve realworld and mathematical problems.
The Number System:
 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and
divide rational numbers.
 Know that there are numbers that are not rational and approximate them by rational numbers.
Expressions and Equations:
 Use properties of operations to generate equivalent expressions.
 Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Geometry:
 Draw, construct and describe geometrical figures and describe the relationships between them.
 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
LOS ANGELES UNIFIED SCHOOL DISTRICT
Division of Special Education
Grade 8
Algebra 1
Geometry
 Solve real-life and mathematical problems involving volume of cylinders, cones, and spheres.
Statistics and Probability:
 Use random sampling to draw inferences about a population.
 Draw informal comparative inferences about two populations.
 Investigate chance processes and develop, use, and evaluate probability models.
The Number System: Know that there are numbers that are not rational, and approximate them by
rational numbers.
Expressions and Equations:
 Work with radicals and integer exponents.
 Understand the connection between proportional relationships, lines, and linear equations.
 Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions:
 Define, evaluate, and compare functions.
 Use functions to model relationships between quantities.
Geometry:
 Understand congruence and similarity using physical models, transparencies, or geometry software.
 Understand and apply the Pythagorean theorem.
 Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Statistics and Probability
 Investigate patterns of association in bivariate data.
The Real Number System:
 Extend the properties of exponents to rational exponents.
 Use properties of rational and irrational numbers.
Quantities: Reason quantitatively and use units to solve problems.
Seeing Structure in Expressions:
 Interpret the structure of expressions.
 Write expressions in equivalent forms to solve problems.
Arithmetic with Polynomials and Rational Expressions: Perform arithmetic operations on polynomials.
Creating Equations: Create equations that describe numbers or relationships.
Reasoning with Equations and Inequalities:
 Understand solving equations as a process of reasoning and explain the reasoning.
 Solve equations and inequalities in one variable.
 Solve systems of equations.
 Represent and solve equations and inequalities graphically.
Interpreting Functions:
 Understand the concept of a function and use function notation.
 Interpret functions that arise in applications in terms of the context.
 Analyze functions using different representations.
Building Functions:
 Build a function that models a relationship between two quantities.
 Build new functions from existing functions.
Linear, Quadratic, and Exponential Models:
 Construct and compare linear, quadratic, and exponential models and solve problems.
 Interpret expressions for functions in terms of the situation they model.
Interpreting Categorical and Quantitative Data:
 Summarize, represent, and interpret data on a single count or measurement variable.
 Summarize, represent, and interpret data on two categorical and quantitative variables.
 Interpret linear models.
Congruence:
 Experiment with transformations in the plane.
 Understand congruence in terms of rigid motions.
LOS ANGELES UNIFIED SCHOOL DISTRICT
Division of Special Education
 Make geometric constructions.
 Prove geometric theorems.
Expressing Geometric Properties with Equations:
 Use coordinates to prove simple geometric theorems algebraically.
 Translate between the geometric description and the equation for a conic section.
 Use coordinates to prove simple geometric theorems algebraically.
Similarity, Right Triangles, and Trigonometry:
 Understand similarity in terms of similarity transformations.
 Prove theorems involving similarity.
 Define trigonometric ratios and solve problems involving right triangles.
Circles:
 Understand and apply theorems about circles.
 Find arc lengths and areas of sectors of circles.
Geometric Measurement and Dimension:
 Explain volume formulas and use them to solve problems.
Assessments
Assessments are embedded in the curriculum provided by the LAUSD Division of Special Education and are a
required element of the course.